The son of Orren Arms Curtis, a soldier, and Ellen Gonville Pappan, who was one-quarter Kansa Indian, Curtis spent his early youth with the Kaw Indian tribe. After being admitted to the bar (1881), he practiced law in Topeka and served as county attorney of Shawnee County from 1884 to 1888. Entering Republican Party politics, he served in the United States House of Representatives (Representatives, House of) (1893–1907) and then in the Senate (1907–13; 1915–29), where he was Republican whip (1915–24) and majority leader (1924–29). Although he opposed Hoover for the Republican presidential nomination in 1928, Curtis won second place on the party ticket, and both men were elected in a landslide electoral vote, 444 to 87. However, he wielded little power as vice president and rarely attended cabinet meetings.

Defeated for reelection in 1932, he returned to the practice of law in Washington, D.C.